Steps To Reproduce

sage: g = AbelianGroup([6])
sage: h = g.permutation_group()
sage: g.is_isomorphic(h)
False

However, h really is a cyclic group of order 6, so is isomorphic to g:

sage: h.is_cyclic()
True
sage: h.order()
6

Expected Behavior

g.is_isomorphic(h) should return True.

Actual Behavior

It returns False.

Additional Information

Possibly related issues are #39890 and #17620

Environment

• OS: Fedora 41
• Sage Version: 10.6.beta9

Checklist

• I have searched the existing issues for a bug report that matches the one I want to file, without success.
• I have read the documentation and troubleshoot guide